Subdifferentials and stability analysis of feasible set and pareto front mappings in linear multiobjective optimization
- Authors: Cánovas, Maria , López, Marco , Mordukhovich, Boris , Parra, Juan
- Date: 2020
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics Vol. 48, no. 2 (2020), p. 315-334
- Relation: http://purl.org/au-research/grants/arc/DP180100602
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- Description: The paper concerns multiobjective linear optimization problems in
- Description: Funding details: European Commission, EC Funding details: European Regional Development Fund, FEDER Funding details: Australian Research Council, ARC Funding details: Australian Research Council, ARC, DP180100602 Funding details: Australian Research Council, ARC, DP-190100555 Funding details: Air Force Office of Scientific Research, AFOSR, 15RT04 Funding details: DMS-1512846, DMS-1808978 Funding text 1: This research has been partially supported by grants MTM2014-59179-C2-(1,2)-P and PGC2018-097960-B-C2(1,2) from MINECO/MICINN, Spain, and ERDF, “A way to make Europe”, European Union. Funding text 2: Research of the second author is also partially supported by the Australian Research Council (ARC) Discovery Grants Scheme (Project Grant # DP180100602). Funding text 3: Research of third author was partially supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research grant #15RT04, and by Australian Research Council under grant DP-190100555.
Calmness of the feasible set mapping for linear inequality systems
- Authors: Cánovas, Maria , López, Marco , Parra, Juan , Toledo, Javier
- Date: 2014
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 22, no. 2 (2014), p. 375-389
- Relation: http://purl.org/au-research/grants/arc/DP110102011
- Full Text: false
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- Description: In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system's data.